After having been elected, Onn met with the then Prime Minister David Cameron, to discuss the future of a Grimsby seafood firm, Young's Seafood, which was due to cut hundreds of jobs after losing a major contract to Sainsbury's.[11] Onn successfully negotiated £1.3 million for the site, helping to keep jobs in Grimsby.[citation needed]

Onn is an advocate of the renewable energy industry and has worked to promote the industry in Grimsby, which Tom Bawden in a 2016 article in The Independent newspaper described as the 'renewable energy capital of England'.[12]

On 20 July 2015, she abstained from the vote on the Conservative government'sWelfare Reform and Work Bill, which restricted child benefit to the first two children in a family and lowers the benefit cap from £26,000 to £20,000 per household.[13] The bill was voted through by 308 to 124 Members of Parliament, despite 48 Labour MPs disobeying the party line of abstention by voting against the bill.[14]

In September 2015, Onn was appointed Shadow Deputy Leader of the House of Commons, working alongside Shadow Leader Chris Bryant.[15]

Onn campaigned for Britain to remain in the European Union, despite her constituency ultimately voting to leave by one of the largest margins in the country.[16][17] Following the result, she voted in the House of Commons to trigger Article 50 of the Treaty on European Union, the process by which member states may withdraw from the European Union, stating that it would be ‘wrong’ to attempt to block the outcome of the referendum.[18] In September 2017, she voted against the EU Withdrawal Bill, in line with the Labour party whip.[19]

She was among many shadow ministers from Labour's frontbench to resign in summer 2016. In her 27 June letter of resignation as Shadow Deputy Leader of the Commons, she told Jeremy Corbyn that the party would remain divided as long as he stayed in post.[20]

On 3 July 2017, she returned to the Labour front bench in the position of Shadow Housing Minister.[23]

In March 2018, Onn suggested a change in law in order to classify wolf-whistles and cat-calls as hate crimes. In response to criticism, she defended her campaign and said there was a problem in Grimsby relating to attitudes towards women and relationships.[24][25]

On 27 March 2019, she resigned from the Labour front bench for a second time to vote against a second Brexit referendum.[26]

Onn is a campaigner to change the law to give greater protection to alleged rape victims. Following the R v Evans case, she said that "going through the victim’s sexual history is much more likely to put people off reporting".[27] She is also an Ambassador for the kinship care charity Mentor and is a supporter of the Family Rights Group.[28]